Grade: 8 Unit: 2 Week: 1 Dates: 10/1-10/5 Content: Scientific Notation and Operations with Scientific Notation Theme Essential Question: How do the nature of expressions and the number system portray mathematics as a science of structure?
Essential Questions: How can you use scientific notation to express very large and very small quantities?
Standards
8. EE.3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.
8. EE.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Objectives
The student will express numbers in scientific notation and standard notation.
The student will compare and order numbers written in scientific notation.
The student will find products and quotients of numbers expressed in scientific notation.
The student will apply technology to their knowledge of scientific notation.
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team The next few weeks are dedicated to expanding the number system. In addition to continuing with the Mathematical Practices already introduced, we need to move forward with the discussion of precision, Mathematical Practice #6.
We suggest that you provide students the opportunity to incorporate the skills already learned with the lesson associated with the number system while looking at precision.
For Example: Simplify (2 x 104 + 4 x 104)2, student incorrect 2 x 104 + 4 x 104 = 8 x 104 = (8 x 104)2 = 64 x 108 = 6.4 x 109. If we apply the transitive property, there is not a legitimate argument since 2 x 104 + 4 x 104 ≠ 6.4 x 109.
Use Mathematical Practice #6 to bring students ability to discuss with accuracy, communicate precisely, use clear definitions, calculate accurately and efficiently, express numerical answers precisely, and be able to carefully formulate an explanation. It has been a building process, but the overlaps and interconnections between the Mathematical Practices are obvious.
As noted in lesson 1-6, expanded form and the connection to place value is important for helping students make sense of scientific notation, which allows very large and very small numbers to be written concisely, enabling easy comparison. To develop familiarity, go back and forth between standard notation and scientific notation. Provide experiences comparing numbers in scientific notation and one given in scientific notation and the other is given in standard notation. Real-world problems can help students compare quantities and make sense about their relationship. Assessment Product
At the end of lesson 1-6, students will conduct research and prepare a class presentation to support moving a city population due to the natural disaster, based on the movie, “Day after Tomorrow” or any other similar type movie. Note: This product is an adaption from the OnCore, Problem solving Connections, pages 27-30.
Key Questions
How are very large or very small numbers changed between scientific and standard notation?
How do we apply our skills of the Laws of Exponents to scientific notation?
How do we apply our understanding of the order of operations to scientific notation?
Observable Student Behaviors
Students will incorporate with and without technology the concept of scientific notation as needed to express very small or very large numbers.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary Scientific notation, properties of exponents, Product Rule, Quotient Rule, Power Rule
Suggested Activities [see Legend to highlight MCO and HYS]
Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 1-2, p. 7-14
ABC Mastering the Common Core in Mathematics Chapter 2-1 through 2-7, p.12-20
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions. Diverse Learners Odyssey (teacher discretion)
Skills Tutor (teacher discretion)
Algebra’scool: Unit D Module 11.2 Homework See corresponding assignment from Suggested Activities
Other Activities, etc. Cell Size and Scale http://sciencenetlinks.com/tools/cell-size-and-scale/
This simple interactive from the University of Utah's Genetic Science Learning Center gives you the opportunity to see how various small things compare to one another. Starting with a Times 12-point font and a coffee bean, scroll along to see how much larger they are than a grain of salt, a human egg, an antibody, and, finally, a carbon atom. Also, included are some reference materials about various ways to measure the size of small things—from meters all the way down to picometers (10-12 m)—and about how such small things can best be viewed
Grade: 8 Unit: 2 Week: 1 Dates: 10/1-10/5
Content: Scientific Notation and Operations with Scientific Notation
Theme Essential Question:
How do the nature of expressions and the number system portray mathematics as a science of structure?
Essential Questions:
How can you use scientific notation to express very large and very small quantities?
Standards
Objectives
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team
The next few weeks are dedicated to expanding the number system. In addition to continuing with the Mathematical Practices already introduced, we need to move forward with the discussion of precision, Mathematical Practice #6.
We suggest that you provide students the opportunity to incorporate the skills already learned with the lesson associated with the number system while looking at precision.
For Example: Simplify (2 x 104 + 4 x 104)2, student incorrect 2 x 104 + 4 x 104 = 8 x 104 = (8 x 104)2 = 64 x 108 = 6.4 x 109. If we apply the transitive property, there is not a legitimate argument since 2 x 104 + 4 x 104 ≠ 6.4 x 109.
Use Mathematical Practice #6 to bring students ability to discuss with accuracy, communicate precisely, use clear definitions, calculate accurately and efficiently, express numerical answers precisely, and be able to carefully formulate an explanation. It has been a building process, but the overlaps and interconnections between the Mathematical Practices are obvious.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
http://www.azed.gov/wp-content/uploads/PDF/MathGr8.pdf
(Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 )
3247.568=3∙103 + 2∙102 + 4∙101+ 7∙100 + 5∙10−1+ 6∙10−2 + 8∙10−3
As noted in lesson 1-6, expanded form and the connection to place value is important for helping students make sense of scientific notation, which allows very large and very small numbers to be written concisely, enabling easy comparison. To develop familiarity, go back and forth between standard notation and scientific notation. Provide experiences comparing numbers in scientific notation and one given in scientific notation and the other is given in standard notation. Real-world problems can help students compare quantities and make sense about their relationship.
Assessment
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Scientific notation, properties of exponents, Product Rule, Quotient Rule, Power Rule
Suggested Activities [see Legend to highlight MCO and HYS]
- Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 1-2, p. 7-14
- ABC Mastering the Common Core in Mathematics Chapter 2-1 through 2-7, p.12-20
- Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
- 8.EE.3- Activity 1 p. 162, Activity 2 p. 163
- 8.EE.4- Activity 1 p. 166, Activity 2 p. 167
- JBHM Unit 1 153-174
- Glencoe PreAlgebra, Chapter 4, p.186-190
- Glencoe Algebra I, Chapter 8, p.425-429
Highly Recommended:- http://illustrativemathematics.org/illustrations/476 (EE.3)
- http://illustrativemathematics.org/illustrations/113 (EE.4)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Diverse Learners
Odyssey (teacher discretion)
Skills Tutor (teacher discretion)
Algebra’scool: Unit D Module 11.2
Homework
See corresponding assignment from Suggested Activities
Terminology for Teachers
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources
Professional Texts
Literary Texts
Informational Texts
- See New York Common Core Aligned Task (other resources)
http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htmArt, Music, and Media
Manipulatives
Games
Videos
SMART Board Lessons, Promethean Lessons
SMART Board Resource Website SMART Board lesson search engine
Websites
Other Activities, etc.
Cell Size and Scale
http://sciencenetlinks.com/tools/cell-size-and-scale/
This simple interactive from the University of Utah's Genetic Science Learning Center gives you the opportunity to see how various small things compare to one another. Starting with a Times 12-point font and a coffee bean, scroll along to see how much larger they are than a grain of salt, a human egg, an antibody, and, finally, a carbon atom. Also, included are some reference materials about various ways to measure the size of small things—from meters all the way down to picometers (10-12 m)—and about how such small things can best be viewed
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